Michael is 4 times as old as Jessica. Fifteen years ago, Michael was 9 times as old as Jessica. How old is Michael now?
Answer: We can use the given information to write down two equations that describe the ages of Michael and Jessica. Let Michael's current age be $m$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $m = 4j$ Fifteen years ago, Michael was $m - 15$ years old, and Jessica was $j - 15$ years old. The information in the second sentence can be expressed in the following equation: $m - 15 = 9(j - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = m / 4$ . Substituting this into our second equation, we get: $m - 15 = 9($ $(m / 4)$ $- 15)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 15 = \dfrac{9}{4} m - 135$ Solving for $m$ , we get: $\dfrac{5}{4} m = 120$ $m = \dfrac{4}{5} \cdot 120 = 96$.